Problem: Simplify the following expression: $ p = \dfrac{9}{8} - \dfrac{-2n}{n + 7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{n + 7}{n + 7}$ $ \dfrac{9}{8} \times \dfrac{n + 7}{n + 7} = \dfrac{9n + 63}{8n + 56} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-2n}{n + 7} \times \dfrac{8}{8} = \dfrac{-16n}{8n + 56} $ Therefore $ p = \dfrac{9n + 63}{8n + 56} - \dfrac{-16n}{8n + 56} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{9n + 63 + 16n }{8n + 56} $ Distribute the negative sign: $p = \dfrac{9n + 63 + 16n}{8n + 56}$ $p = \dfrac{25n + 63}{8n + 56}$